Question

5 -letter "words" are formed using the letters A, B, C, D, E, F, G. How many such words are possible for each of the following conditions?

a) No condition is imposed.  

b) No letter can be repeated in a word.

c) Each word must begin with the letter A.

d) The letter C must be at the end.  

e) The second letter must be a vowel.

Answer 1

a) Number of letters = 7

Number of 5 letter words possible, with no conditions imposed =

= 16,807

b) Number of 5 letter words possible, with no repetition = 7P5

= 7!/(7-5)!

= 7 x 6 x 5 x 4 x 3

= 2520

c) Number of 5 letters words possible if each word must begin with A = 1 x

= 2401

d) Number of 5 letters words possible if the letter C must be at the end = Number of 4 letter words without C x Number of options for last letter
(It is not necessary that the last letter is C)

=

= 9072

e) Number of options for second letter = 2 (A and E)

Number of options for other 4 letters = 7

Number of words possible if the second letter must be a vowel =

= 4802